On the macro-economic impacts of climate change under cognitive limitations Alexandre Gohin ...

24 Pages·2014·0.16 MB·English

On the macro-economic impacts of climate change under cognitive limitations
Alexandre Gohin and Ruixuan Cao
UMR SMART Rennes
Corresponding author: [email protected]
April 2014
Paper submitted to the Global Trade Analysis Conference, Dakar

Abstract
Although the sources, extent and physical impacts of the future climate change are highly uncertain,
available dynamic economic assessments implicitly assume that economic agents perfectly know
them. Perfect foresight, rational expectations or active learning are standard assumptions underlying
simulated results. To the contrary, this paper builds on the assumption that economic agents may
suffer for a while from limited knowledge about the average and variability of physical impacts of
climate change. Using a world dynamic and stochastic general equilibrium model, our simulation
results show that identifying the average physical impact is much more crucial than its variability. This
finding is robust to the level of risk aversion of economic agents. The rate of pure time preference of
economic agents more significantly affects the economic impacts. Because we exclude exogenous
economic growth, we find that it is better to learn earlier the physical impacts of the climate change.

Keywords: climate change, DSGE model, informational limitations
Introduction
Available assessments of the future economic impacts of the climate change are still highly divergent.
Estimates of the average yearly welfare impact of the climate change range from an optimistic
increase of the world GDP by 2.5 per cent (taken from Tol, 2009) to a pessimist decrease by as much
as 20 per cent (computed in the Stern review, 2006). Many modeling assumptions contribute to these
different figures, such as the highly disputed discount rate used in standard Cost Benefit Analysis
(CBA) to balance future impacts relative to current expenditures (see for instance, Gollier, 2010 or
Gollier and Weitzman, 2010).
These economic assessments are now mostly performed within stochastic contexts. Indeed most first
economic researches adopt determinist economic approaches and thus focus on the average
consequences. However it has always been recognized that there are many unknowns on the different
future sources of greenhouse gas (GHG), on the climate sensitivity to GHG changes or on the physical
damages of some climate changes (see for instance, Malik et al. 2010). Accordingly, many recent
economic researches introduce stochastic dimensions in their framework.
We can distinguish three main stochastic approaches developed so far to assess the climate change
issue. The first approach consists in performing sensitivity analysis (for instance with Monte-Carlo
simulations) of the modeling results to the values of some behavioral parameters, exogenous variables
or scenario assumptions. This first approach includes all dynamic deterministic economic models
where the behavior of economic agents does not acknowledge the presence of stochastic variables (the
certainty equivalence assumption is applied) or where the economic agents are supposed to have
perfect foresight (they know the future values of all stochastic variables). The majority of present
economic researches can be gathered in this first simple approach. A prominent example is the
analysis performed by Nordhaus (2007) with the widely used Dynamic Integrated model of Climate
and the Economy (DICE) which is an Integrated Assessment Model (IAM) coupling climate equation
with a stylized dynamic, determinist, general equilibrium model.
While widely perceived as useful, this first approach suffers from the absence of behavioral responses
of economic agents to the stochastic variables. To the contrary, the second and third approaches allow
economic agents to optimize taking some of them into account. In the second approach, economic
agents are supposed to have full information on the structural parameters and the stochastic variables
(the density function and the corresponding moments). They furthermore have rational expectations.
To our knowledge, few papers so far adopted this approach.1 By chronological order, these papers
include Pizer (1999) who introduces (log normal) labor productivity shocks but imposes a first order
approximation on the optimal behavior of economic agents (hence ignoring in fine their risk aversion),
Bostian and Golub (2008) who solve a stochastic version of the DICE model assuming risk aversion
and (log normal) total factor productivity shock, Bukowski and Kowal (2010) who develop a multi-
sector Dynamic and Stochastic General Equilibrium (DSGE) model for Poland with risk averse agents
and many productivity and external (normal) shocks, Hwang et al. (2011) who again solve a stochastic
version of the DICE model assuming that the climate sensitivity parameter is stochastic (with different
density functions but otherwise the model is not stochastic, so the true stochastic source is unclear),
Crost and Traeger (2011) who introduce the same stochastic dimension in the DICE model in the same
manner while distinguishing risk aversion from resistance to inter-temporal substitution, Golosov et al.
(2012) who solve a stylized DSGE model close to DICE while imposing exogenous ad hoc saving
functions in order to obtain analytic solutions (again without a clear source of the stochastic variable)
and finally Dumas et al. (2012) where they assume only one stochastic period (with two stochastic
event at that period).
In the third approach, economic agents are supposed to have initially only incomplete information on
some structural parameters or stochastic variables while full information on the other structural
parameters or stochastic variables. But they are assumed to be able to learn at each period and recover
full information on all structural parameters and stochastic variables in the (very) long run. When the
additional assumption of rational (active) learning with cost-free periodic information is made, then
economic agents solve an additional tradeoff between the benefit of controlling emissions and of
getting more information when optimizing their abatement efforts. Kelly and Kolstad (1999)
pioneered such approach starting from the DICE model. They assume that the average annual global
temperature is stochastic (the error term is normal) with the level of GHG as a determinant. The
climate sensitivity parameter, which relates the two variables, is unknown to economic agents. They
have only priors on this parameter but are able to progressively learn it using a Bayesian updating
procedure applied on periodic observations of temperature and GHG levels. These authors conclude
that over 90 years are required to learn the true structural parameters. Leach (2007) expands this
analysis adding the assumption that the economic agents also do not know the parameter governing

1 One reason may be that they were until recently some computational issues to solve large scale dynamic and
stochastic models.
the persistence of natural trends in the same global temperature equation. He concludes that the time to
learn the true structural parameters may be in the order of thousands of years. The paper of Karp and
Zhang (2006) is slightly different as they assume that all structural parameters are perfectly known
while some stochastic variables are only partially known. More precisely, these authors develop a
simpler economic model with linear-quadratic abatement costs and environmental damages, risk-
neutral agents and three (log normal) stochastic sources: one on the marginal benefit of emissions for
the regulator (due to the asymmetric information between the regulator and economic agents) and two
on the marginal damage function (to both the regulator and economic agents). The moments of two of
them are perfectly known and the last one (on the marginal damage) is recovered through passive
learning (assumption which fits best with the risk neutrality assumption). They show as expected that
the variance of the known shock in the marginal damage function has major impacts on the learning
process. If this variance is significant, then periodic observation brings limited information and
learning on the unknown marginal damage shock is slow. In this case the anticipation of learning has a
negligible effect on the optimal policy.
With respect to this growing literature on climate change and uncertainty, our main contribution is to
authorize economic agents to have and stay, at least temporary, with incomplete information about the
different stochastic sources they are facing. This leads us to develop a fourth approach allowing
(temporary) imperfect foresights by economic agents. This issue has been widely disregarded so far
(Tol, 2009) or only discussed qualitatively. For instance, Hallegate et al (2007) conclude from their
deterministic computations that the costs of climate change under imperfect foresight are drastically
increased when compared to a perfect foresight situation. Just (2001) also argue qualitatively that
economists need to address the changing nature of uncertainty (in agriculture) and that continuing to
ignore Knigthain uncertainty is leading empirical economic analysis away from policy relevance.
Our main contribution is first motivated by the fact that the climate is far from being the only
stochastic source faced by many economic sectors. For instance, Nordhaus (2007) finds from DICE
simulations that by far the most important uncertain variable for climatic outcomes is the growth in
total factor productivity and not the temperature sensitivity coefficient. Lobell and Burke (2008)
provide a more concrete justification. They argue that major progresses in understanding crop yield
responses to change of mean temperature or precipitation levels are still expected with experimental
tests. Moreover these authors find that the single biggest source of uncertainty for most crop yields
comes from the uncertainty in the response of crop production to the mean temperature change,
followed by the uncertainty on the mean temperature change itself. This major uncertainty of these
crop yield responses is simply ignored in aforementioned analyses because factor productivity shocks,
when introduced, are exogenous to the climate variables. Our main point here is that it will be very
difficult for economic agents (farmers in this instance) to quickly understand the evolution of their
total productivity. They may be unable in the first years to discern the climate change impacts from
other stochastic sources and hence may not take optimal adaptation/learning decisions. This point
echoes the Karp and Zhang result that learning is not worthy when simultaneously other stochastic
sources are important.
Our contribution is also motivated by some theoretical results on the decision making modeling under
uncertainty (they are obtained in the context of a single stochastic source but remain relevant with
many stochastic variables). Geweke (2001) shows that the very existence of the expected utility is not
ensured in many cases. More precisely, he demonstrate that the expected utility of a risk averse
economic agent endowed with a CRRA utility (log utility aside) often fails to exist when the stochastic
consumption is log normal with an unknown second moment. This statistical result leads this author to
conclude that the standard rational expectations assumption (that agents know the relevant
distributions or that they are able to learn it) is quite fragile.i The implication for our paper is that it is
inconsistent to assume, as previous papers did in the third approach, that economic agents are able to
immediately learn from climate observations while assuming they have CRRA utility functions.
Weitzman (2009) builds on the same statistical result to show that the fat tail consumption distribution
induced by the unknown climate change variability leads to an infinite expected value of the stochastic
discount factor. This infinite value implies that economic agents should postpone any unit of current
consumption to mitigate future catastrophe. Weitzman (2009) solves this issue by introducing a lower
bound on consumption which is exogenously calibrated using a value of a statistical life. Ikefuji et al.
(2011) solve this issue by assuming other utility functions (exponential and Pareto) and solving their
two period models by backward inductions (hence with the debatable assumption that terminal
conditions must be arbitrarily imposed). McKitrick (2012) shows that this unbounded stochastic
discount factor does not emerge with contingent goods. However he simply assumes the existence of
such goods and markets for the long run. In our paper, we do not solve theoretically these different
informational issues (using alternative utility functions or alternative decision theory under uncertainty
or an augmented micro-structure). Rather we want to offer relative estimates of the extent of these
informational issues, relative to those obtained with full/perfect information.
In that respect we develop a stylized DSGE model without always imposing the standard rational
expectations/perfect foresight assumptions (hence our model can also be viewed as an Agent based
model). Our starting modeling point is close to the often-used DICE model with the same major
economic mechanisms included. However we simply ignore the climate change equations explaining
the sources of the environmental damage and the anthropogenic contribution for two main reasons.
First, Bostian and Golub (2010) elegantly recognize that solving a stochastic version of the full DICE
model remains today quite challenging (with perturbation methods possibly leading to spurious
welfare reversals). By removing the climate equations, we reduce the number of state variables and no
longer face computational issues. Second, this assumption is not crucial for our analysis as we
consider that many other stochastic sources unrelated to the climate affect the industrial factor
productivities and are also unexplained. Our modeling simplification prevents us to perform a policy
analysis on the optimal carbon tax in order to reduce current GHG emissions and future damage. In
other words, our analysis excludes mitigation options and focus on adaptation strategies under
different informational assumptions. We can also view our analysis more relevant in the short to
medium run where climate change results from past irreversible decisions due to the (several decades)
delay between emissions and impacts.
On the other hand, our economic modeling is less stylized than the DICE one because we introduce
two production sectors rather than only one. Otherwise, our assumption of incomplete information by
economic agents appears less relevant. We suppose the existence of three representative economic
agents. The first two are owners of the capital goods used in the two production sectors while the third
only have their labor force. We develop three of our model. They are all calibrated on the same Social
Accounting Matrix (SAM) built from the GTAP database for 2004. In the first determinist version, we
assume that economic agents perfectly know from the first period to the last one all structural
parameters and exogenous variables. This version can be simulated assuming different exogenous
variables reflecting the imperfect knowledge of the modeler of the impact of climate change on factor
productivities or even the imperfect knowledge of factor productivities without climate change. This
first determinist version falls within the first stochastic approach that we identify in the literature on
climate change. In the second stochastic version, we assume that all economic agents perfectly know
the structural parameters, exogenous variables and the distribution of stochastic variables: the
productivity shocks in both sectors both with and without the climate change. In addition, they have
rational expectations and thus are able to compute market equilibrium once the values of productivity
shocks are revealed. This second version falls within the second approach identified in the literature.
The third and last version is again stochastic where we assume that all economic agents suffer from
informational failures. They are unable during some periods to identify the stochastic technological
impacts of the climate change. By comparing the results of the second and third versions, we will be
able to assess the value of information on the true extent of physical impacts of climate change
(resulting from past decisions).
This paper is organized as follows. The next section details the specification of the three versions of
our model starting from the simple determinist version close to DICE. We also explain the calibration
of the different structural parameters. The following section reports the results of illustrative
simulations. Market and welfare effects are simultaneously discussed. Sensitivity analyses of results to
the level of risk aversion of economic agents and to the variability of the physical impacts of climate
change are provided in a third section. The paper concludes with some methodological and normative
recommendations.

1. Methodological frameworks
The three versions of our model differ in the information held by economic agents. We start with the
simplest version where economic agents have perfect information on all behavioral parameters and
future exogenous variables. While presenting this first version, we explicit the several simplifying
assumptions we make in order to focus on the informational issues related to the extent of climate
change physical impacts.

1.1. The perfect foresight version
Assumptions
We consider a simple (world) economy populated with three different types of economic agents. The
first and second types of economic agents represent the households that own capital assets, decide the
levels of production, intermediate uses, investments, unskilled labor demands and their own final
consumptions subject to technological, capital accumulation and budget constraints. We rule out for
simplicity a labor-leisure choice and assume that these economic agents fully allocate their skilled
labor in their respective production. The main difference between these two economic agents/sectors is
that the second one is producing a composite good that is also used for the formation of the capital. In
the empirical part of the paper, we will group farm and food producers in the first type and other
producers (manufacture and service) in the second type. As usual, we assume representative agents
with infinite horizons, (restrictive) Cobb Douglas periodic preferences and production functions. We
also adopt an additive time structure in the overall utility function and thus assume that the risk
aversion parameter equals the resistance to inter-temporal substitution (the rate of pure time preference
is constant). The third type gathers economic agents who do not own capital assets. These economic
agents, that we label unskilled workers for the rest of this paper, sell their labor endowment to
productive sectors at the wage rate and consume the two products available on the markets. Their only
periodic decision is the optimal allocation of their income to the final consumption of these two goods
(so no labor-leisure choice, no saving).
We make the heroic assumption that a (world)social planner exists and optimizes allocation of scarce
resources to maximize total economic welfare. This assumption is usually made, such as in the
standard DICE model. It avoids us to deal with the possible different information structure held by the
different economic agents (and the micro structure with contingent markets) and consequently the
distributive issues.
Analytical derivation
Formally, the program of the social planner is given by
∞
(cid:24) (cid:16)(cid:17) (cid:11)(cid:10)(cid:16)(cid:17) (cid:11)(cid:10)(cid:20)(cid:17)
(cid:9)(cid:10)(cid:11)(cid:13)(cid:14)(cid:11)(cid:15)(cid:9)(cid:14)(cid:18)(cid:15)(cid:9) (cid:19)
(cid:1)(cid:2)(cid:3) (cid:5) = (cid:7)(cid:7)(cid:8)
1−(cid:23)(cid:15)
(cid:15)(cid:12)(cid:11)(cid:9)(cid:12)(cid:11)
(cid:24) (cid:18)

(cid:25).(cid:27).(cid:7)(cid:14)(cid:11)(cid:15)(cid:9)+(cid:7)(cid:29)(cid:14)(cid:11)(cid:15)(cid:9) ≤ (cid:31)(cid:11)(cid:9) = !"(cid:11)(cid:9)#$(cid:11)(cid:9)%(cid:16)&’#((cid:11)(cid:9)%(cid:16))’#(cid:29)(cid:14)(cid:11)(cid:11)(cid:9)%(cid:16)*+’’#(cid:29)(cid:14)(cid:18)(cid:11)(cid:9)%(cid:16)*+,’#.-.(.(cid:11)%(cid:16)/)’
(cid:15)(cid:12)(cid:11) (cid:15)(cid:12)(cid:11)
(cid:24) (cid:18)

(cid:25).(cid:27).(cid:7)(cid:14)(cid:18)(cid:15)(cid:9) +(cid:7)0(cid:29)(cid:14)(cid:18)(cid:15)(cid:9) +(cid:29)(cid:15)(cid:9)1≤ (cid:31)(cid:18)(cid:9) = !"(cid:18)(cid:9)#$(cid:18)(cid:9)%(cid:16)&,#((cid:18)(cid:9)%(cid:16)),#(cid:29)(cid:14)(cid:11)(cid:18)(cid:9)%(cid:16)*+’,#(cid:29)(cid:14)(cid:18)(cid:18)(cid:9)%(cid:16)*+,,#-..(.(cid:18)%(cid:16)/),
(cid:15)(cid:12)(cid:11) (cid:15)(cid:12)(cid:11)

(cid:25).(cid:27). $(cid:15)(cid:9)2(cid:11) ≤ $(cid:15)(cid:9)01−3(cid:15)1+(cid:29)(cid:15)(cid:9), $(cid:15)(cid:11) = $5(cid:15)(cid:11) 6 = 1,2
(cid:18)

(cid:25).(cid:27).(cid:7)((cid:15)(cid:9) ≤ (.(cid:9)
(cid:15)(cid:12)(cid:11)
The first constraint of this optimization program captures the market equilibrium condition for “food”
products. The second one pertains to the manufactured products and includes the investment demands
in the left hand side. The third constraint captures the capital accumulation constraint and finally the
last one the equilibrium constraint on the unskilled labor market. Assuming interior solutions we can
incorporate the capital accumulation constraints in the market equilibrium conditions for manufactured
products. The program then reduces to three constraints and three multipliers (the discounted prices of
goods and the wages at each period).
The first order conditions are given by:
(cid:16)(cid:17) (cid:11)(cid:10)(cid:16)(cid:17) (cid:11)(cid:10)(cid:20)(cid:17) (1)
(cid:15)(cid:13)(cid:14)(cid:11)(cid:15)(cid:9)(cid:14)(cid:18)(cid:15)(cid:9) (cid:19) = 89(cid:9)(cid:14)9(cid:15)(cid:9),: = 1,2,6 = 1,3,(cid:27) = 1,∝
(2)
=>9(cid:15)8(cid:15)(cid:9)(cid:31)(cid:15)(cid:9) = 89(cid:9)(cid:29)(cid:14)9(cid:15)(cid:9),: = 1,2,6 = 1,2,(cid:27) = 1,∝
(3)
?(cid:15)8(cid:15)(cid:9)(cid:31)(cid:15)(cid:9) = @(cid:9)((cid:15)(cid:9),6 = 1,2,(cid:27) = 1,∝
"(cid:17)CD’ (4)
8(cid:18)(cid:9) = (cid:8)A01−3(cid:15)18(cid:18)(cid:9)2(cid:11)+8(cid:15)(cid:9)2(cid:11) B(cid:15) E,6 = 1,2,(cid:27) = 1,∝
B(cid:17)CD’
Equation (1) expresses the optimal final demands of goods by the three agents. Equation (2) expresses
the optimal intermediate demand of goods by producing activities, equation (3) their optimal labor
demands. Finally equation (4) expresses the optimal evolution of the capital stocks in the two
producing sectors. As usual, the optimal capital stock ensured that the marginal cost of capital stock
(the left hand side) equals the marginal benefit (captured by the right hand side). This marginal benefit
includes two terms, the next period depreciated capital stocks and the next period additional
production.
Calibration and resolution
All these first conditions and market equilibrium constraints must be solved simultaneously in order to
determine the optimal evolution of endogenous variables. Exogenous variables are given by the initial
values of capital stocks and the labor endowments and by the technological and preference parameters.
In order to solve this perfect foresight version, we thus need to calibrate all behavioral parameters,
give initial values to the capital stocks and labor endowments and impose some terminal conditions
(due to the Euler type equation 4 involving next period variables). Because we adopt Cobb Douglas
functions, most behavioral parameters and the values of initial stocks can be retrieved from observed
values gathered in a SAM for a given year (such as from the widely used GTAP database) if we
simultaneously assume that the world economy in this year was in a steady state (as usual, we
normalize all prices in this steady state) . The only two parameters we need to impose are the rate of
pure time preference and the risk aversion parameters. In the standard calibration, we assume that
these values are equal across agents and are similar to those used in the standard calibration of the
DICE model. The rate of pure time preference is fixed at 0.015 and the risk aversion parameter to 2.
The SAM used for calibration and the starting point of the model is derived from the GTAP database
with slight adjustments: it is provided in appendix 1. Finally we impose the standard terminal
condition (as in the DICE model) that in the last simulated period, investment equals the depreciation
of capital. The first order condition (4) is thus replaced by
(4’)
(cid:29)(cid:15)F = 3(cid:15)$(cid:15)F
Implementation of scenarios
In order to evaluate the economic impacts of the climate change, we first generate baseline (or without
climate change) results and then rerun the model assuming some physical impacts of the climate
change. We generate different baselines to reflect the uncertainties about factor productivities.
Contrary to Nordhaus (2007) we specify log normal density functions with standard errors equal to
0.05 in both production sectors:

I
ln # "(cid:15)(cid:9)%∼K#0;0.05%
This level of standard errors ensures reasonable volatilities of simulated GDP from the baseline
results. Again it should be clear that future factor productivities may take different values but the
perfect foresight approach, adopted for instance in the DICE model, assume that economic agents
perfectly know from the first period the ones that will materialize in the subsequent periods. Like the
sensitivity analysis performed by Nordhaus (2007) we perform different runs of the model (200
instead of 100). We thus obtain 200 baselines extending over 100 years. We then simulate the impacts
of climate change by assuming that factor productivities take new stochastic values. They reflect the
uncertain physical impacts of previous GHG emissions on current and future factor productivities (due
to lags between physical emissions and impacts). We again specify log normal probability
distributions and assume that the first moment is higher (the double) in the farm sector than in the
manufacturing sector. As regards the standard errors of these new stochastic variables, we will
consider different values and assume initially that they equal 0.05:
O
ln # %∼ K#−0.05;0.05%
"(cid:11)(cid:9)
O
ln # %∼ K#−0.025;0.05%
"(cid:18)(cid:9)
These shocks are not precisely justified as in the Nordhaus analysis. They just ensure that our average
welfare impacts are in the middle of available welfare estimates. We hypothesize that climate changes
on agricultural productivies may be greater than on other industries.